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# Learning Simultaneous Concept in Word Problems

Simultaneous concept normally involved at least two different items. It will be phrased like the one we posted on our Facebook page, as shown below.

Facebook post (3 Mar)

Math Process Skills 3: Simultaneous Concept [P5/P6]

5 similar bags and 4 similar pairs of shoes cost \$701.

2 similar bags and 3 similar pairs of shoes cost \$433.

How much does a pair of shoes cost?

Try #1 (by addition and subtraction) If we add both statements, then we can say that 7 similar bags and 7 similar pairs of shoes cost \$1134. After which we will divide \$1134 by 7 to get the price of 1 bag and 1 pair of shoes, which is \$162. Common error among students: They think that the price of the bag equals the price of the pair of shoes. That is the reason that they will divide \$162 by 2. To prevent such error, we need to remind students that the prices of the bag is different from the pair of shoes.

Thereafter, when we subtract \$162 from \$433, we will get the price of 1 bag and 2 pairs of shoes which is \$271. Then subtract \$162 from \$271 will give us the price of a pair of shoes, which is \$109.

Try #2 (by lowest common multiple and compare) 5 bags and 4 pairs of shoes cost \$701.

2 bags and 3 pairs of shoes cost \$433.

The lowest common multiple of 5 and 2 is 10. Hence, we can say that 10 bags and 8 pairs of shoes cost \$1402. (multiply the first sentence by 2) 10 bags and 15 pairs of shoes cost \$2165. (multiply the second sentence by 5) Now that the number of bags are equal, we can see that 7 pairs of shoes cost \$2165 - \$1402 = \$763. Hence, \$763 divided by 7 will give us \$109, the price of 1 pair of shoes.

We can also solve the problem with the help of the simple program that I have created using google sheets or microsoft excel. We just need to key in the facts in the yellow boxes, the calculation will be done automatically. 